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Pythagoras is Ionian philosopher and Mathematician of 6th century BC , who is also called father of numbers by greek, He established a religion called Pythagoreanism. He is best known for pythagoras theorem. Let us analyze the facts behind Pythagoras theorem.

Pythagoras LegendPythagoras was born on Samos, a Greek island in the eastern Aegean, off the coast of Asia Minor. He was born to Pythais (his mother, a native of Samos) and Mnesarchus (his father, a Phoenician merchant from Tyre). As a young man, he left his native city for Croton, Calabria, in Southern Italy, to escape the tyrannical government of Polycrates. According to Iamblichus, Thales, impressed with his abilities, advised Pythagoras to head to Memphis in Egypt and study with the priests there who were renowned for their wisdom. He also was discipled in the temples of Tyre and Byblos in Phoenicia. It may have been in Egypt where he learned some geometric principles which eventually inspired his formulation of the theorem that is now called by his name.

Pythagoras theorem
Pythagoras is commonly given credit for discovering the Pythagorean theorem, a theorem in trigonometry that states that in a right-angled triangle the square of the hypotenuse (the side opposite the right angle), c, is equal to the sum of the squares of the other two sides, b and a—that is, a² + b² = c².

As this is the contentious topic. Let us find out the truth.

Pythagores school- It is not clear whether he, or his students, have constructed the first proof. Because of the secretive nature of his school and the custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved this theorem. For that matter, there is no evidence that he worked on any mathematical or meta-mathematical problems.

Five centuries after death - Some attribute it as a carefully constructed myth by followers of Plato over two centuries after the death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to Pythagoras. This attribution has stuck, down the centuries up to modern times. The earliest known mention of Pythagoras's name in connection with the theorem occurred five centuries after his death, in the writings of Cicero and Plutarch.

From the Hellenistic period, Greek replaced Egyptian as the written language of Egyptian scholars, and from this point Egyptian mathematics merged with Greek and Babylonian mathematics to give rise to Hellenistic mathematics. Egyptian mathematics also built pyramids , which is proof where these theorems originated. It is not greece, it is Egypt.

From the above points we can see that pythagoras is just a legend, who was made a mathematician to suit greek superiority , which is proved by the gap between the existence and commentry on them much later. The mathematical theories like geometry , numbers , pythagoras theorem was borrowed from Indian, Babylonian and Egypt sources and has been claimed as greek own, eventhough we can say much work was done later by greeks.

Almost all historians have been saying Democracy & Republic originated in West(in greece), the bastion of Free people. Let us see the facts in detail.

India has democracy from early days earlier than Greece

India has democracy at all levels right from village level to state, Not just State level.

It is entirely possible that Democracy travelled from India to Greece.

Teachings of Buddhism and jainism inspire democracy and republicanism , what inspired Greece.

Let us see evidences

First democracy and Republics

Sumerian
Early Sumerian period is said to be democratic between 2900BC to 2300BC , but we have no solid evidence to support the theory, we have only pointers

Indian
Next comes the Indian reference Rig Veda between 4000BC to 2000BC. Which talk of Sabha , samiti to elect the ruler. Ramayana(500BC) also mentions samiti. Vaishali was the capital of the vibrant Republican Licchavi state since before the birth of Mahavira(founder of Jainism- 599 BC), which suggests that it was perhaps the first republic in the world.

The most useful Greek account of India is Arrian's Anabasis of Alexander , which describes the Macedonian conqueror's campaigns in great detail. The Anabasis, which is derived from the eyewitness accounts of Alexander's companions, portrays him as meeting "free and independent" Indian communities at every turn. What "free and independent" meant is illustrated from the case of Nysa, a city on the border of modern Afghanistan and Pakistan that was ruled by a president named Aculphis and a council of 300. After surrendering to Alexander(327BC), Aculphis used the city's supposed connection with the god Dionysus to seek lenient terms from the king

The first-hand description of India by a Greek traveler named Megasthenes. After Alexander's invasion, Megasthenes served as ambassador of the Greek king Seleucus Nicator to the Indian emperor Chandragupta Maurya, and in the course of his duties crossed northern India to the eastern city of Patna, where he lived for a while. If this statement is drawn from Megasthenes, then the picture of a northwestern India dominated by republics must be extended to the entire northern half of the subcontinent.

The most useful sources for mapping north India are three: The Pali Canon, which shows us northeastern India between the Himalayas and the Ganges in the sixth and fifth centuries B.C.; the grammar of Panini, which discusses all of North India, with a focus on the northwest, during the fifth century; and Kautilya's Arthasastra, which is a product of the fourth century, roughly contemporaneous with Megasthenes. All three sources enable us to identify numerous sanghas and ganas, some very minor, others large and powerful.

According to Panini, all the states and Republics (janapadas ) of northern India during his time were based on the settlement or conquest of a given area by an identifiable warrior people who still dominated the political life of that area. Some of these peoples (in Panini's terms janapadins ) were subject to a king, who was at least in theory of their own blood and was perhaps dependent on their special support. Elsewhere, the janapadins ran their affairs in a republican manner. Thus in both kinds of state, the government was dominated by people classified as ksatriyas, or, as later ages would put it, members of the warrior caste.

Kautilya: according to him, there were two kinds of janapadas, ayudhiya-praya, those made up mostly of soldiers, and sreni-praya , those comprising guilds of craftsmen, traders, and agriculturalists. The first were political entities where military tradition alone defined those worthy of power, while the second would seem to be communities where wealth derived from peaceful economic activity gave some access to the political process. This interpretation is supported by the fact that sreni or guilds based on an economic interest were often both part of the armed force of a state and recognized as having jurisdiction over their own members.

The numerous members of a sovereign gana or sangha interacted with each other as members of an assembly. Details of the working of such assemblies can be found both in Brahmanical and Buddhist literature. By the time of Panini (fifth century B.C.), there was a terminology for the process of corporate decision-making. Panini gives us the terms for vote, decisions reached by voting, and the completion of a quorum. Another cluster of words indicates that the division of assemblies into political parties was well known. Further, Panini and his commentators show that sometimes a smaller select group within a sangha had special functions -- acting as an executive, or perhaps as a committees for defined purposes

The rules for conducting the Buddhist sangha were, according to the first chapter of the Maha-parinibbana-suttanta, based in principle on those commonly found in political sanghas or ganas. In the case of the Buddhist sangha, the key organizational virtue was the full participation of all the monks in the ritual and disciplinary acts of their group. To assure that this would be remembered, detailed rules concerning the voting in monastic assemblies, their membership, and their quorums, were set down in the Mahavagga and the Kullavagga . Business could only be transacted legitimately in a full assembly, by a vote of all the members. If, for example, a candidate wanted the upasampada ordination, the question (ñatti) was put to the sangha by a learned and competent member, and the other members asked three times to indicate dissent. If there was none, the sangha was taken to be in agreement with the ñatti. The decision was finalized by the proclamation of the decision of the sangha.

The Pali Canon gives us our earliest, and perhaps our best, detailed look at Indian republicanism, its workings, and its political philosophy. About no other republics do we know as much as we do about the Buddhist sangha and the Licchavis in the time of Buddha even though we do know that republics survived and were a significant factor until perhaps the fourth century A.D., a period of over 800 years. Scattered inscriptions, a great number of coins, and the occasional notice in Greek sources, the Jatakas or other Indian literature give us a few facts.

Greek
Four centuries before the beginning of this millennium, Plato indicted the city-state of Athens for handing over power to the people, for they had neither the inclination nor the training to run their lives. From the 5th century BCE (BC), Athenian democracy gave citizens equal rights to participate in decision making and to hold public office; it was based on the ideal of equality among citizens. One small caveat though - not everyone was a citizen. Only native Athenian men over the age of twenty were eligible for active citizenship. Not the 60 per cent of the Athenian population who were slaves, certainly not women, and not the so-called "immigrants" whose families had settled in Athens several generations earlier. But Plato looked on even this highly restricted citizenship with dismay.

America
Historian Jack Weatherford asserts that Thomas Jefferson, Benjamin Franklin, and others, got their ideas on democracy not from any Greek or Roman influence, but from the Iroquois and other indigenous peoples of the Americas, who practiced the type of democracy found in the United States Constitution, through self-governing territories that were part of a larger whole. This democracy was founded between the years 1000-1450, and lasted several hundred years. He also states that American democracy was continually changed and improved by the influence of Native Americans throughout North America. For example, the right of women to vote started on the American frontier, and moved eastward. In other words, Americans learned democracy from the indigenous peoples of the North America.

Levels of Democracy
Democracy and Republicanism are not same everywhere, Some places we had Rulers being elected, some places councils were elected, some places some regions also have democracies. The next most important thing is levels of participation. We cannot compare todays democracies and republics with yesteryears. But India had mature level of democracy ,which shows deep rooted democratic institutions.

Democracy travelled from East to West.

It is entirely possible that democracy and republicanism travelled from East to west. Since religions in east contemplated renouncing all desires. And also we have suddenly democracy arriving in west. That means import from some where else. All along Greek and Roman intelligentsia are aware of eastern thoughts.

Religious Role
Teachings of Rig veda , Buddhism and jainism created sabhas, samitis and sanghas which were primarily democratic institutions. The monarchy is always weak in India , because of democratic institutions. Empowering of the monarchy happened with Brahminical text Manu and Kautilya arthasastra. For which ruling caste was created and subsequently other castes. Later religious texts like puranas also maintained the primacy of kings until 10th century when both buddhism and jainism were active.

We can see from the above article democracy and Republicanism originated in India and travelled to west.